Hamilton Cycles in Intersection Graphs of Bases of Matroids

DOI

10.2991/mmsa-18.2018.73How to use a DOI?

Keywords

matroid; intersection graph; Hamilton cycle

Abstract

The intersection graph of bases of a matroid M=(E, B) is a graph G with vertex set V(G) and edge set E(G) such that V(G)=B and E(G)=BB', where the same notation is used for the vertices of G and the bases of M, B and B' has no intersection. In this paper, we prove that for any given edge e of G, the intersection graph G of bases of a matroid M with rank at least 2 has a Hamilton cycle containing edge e and another Hamilton cycle avoiding edge e.

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Yinghao Zhang
AU  - Hongmei Chi
PY  - 2018/03
DA  - 2018/03
TI  - Hamilton Cycles in Intersection Graphs of Bases of Matroids
BT  - Proceedings of the 2018 International Conference on Mathematics, Modelling, Simulation and Algorithms (MMSA 2018)
PB  - Atlantis Press
SP  - 331
EP  - 334
SN  - 1951-6851
UR  - https://doi.org/10.2991/mmsa-18.2018.73
DO  - 10.2991/mmsa-18.2018.73
ID  - Zhang2018/03
ER  -